cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A096543 Formed from a secondary diagonal of triangle A096542 where a(n) = A096542(n,n-2)/3.

Original entry on oeis.org

0, 0, 0, 5, 188, 5560, 159460, 4715480, 147031080, 4874069760, 172184044920, 6479888595840, 259376627795780, 11019372206402560, 495710267052627900, 23556524839760174080, 1179771865401761781520, 62133101833103144386560
Offset: 0

Views

Author

Paul D. Hanna, Jun 25 2004

Keywords

Crossrefs

A096544 Formed from a secondary diagonal of triangle A096542 where a(n) = A096542(n,n-3)/4.

Original entry on oeis.org

0, 0, 0, 0, 61, 4385, 219435, 9785650, 423038910, 18400152960, 820149026970, 37821215615040, 1813429065435075, 90623195098916480, 4724647736141458125, 257000193714640346880, 14579739601017142299020, 861991467355420222464000
Offset: 0

Views

Author

Paul D. Hanna, Jun 25 2004

Keywords

Crossrefs

A096537 E.g.f.: A(x) = exp(x*exp(2*x*exp(3*x*exp(...exp(n*x*exp(...))...)))), for n>=1.

Original entry on oeis.org

1, 1, 5, 61, 1377, 49721, 2625313, 190735749, 18246616321, 2223115264945, 336071395603521, 61725395919953789, 13537971184957280449, 3494778862390292571849, 1048886507411306132337889
Offset: 0

Views

Author

Paul D. Hanna, Jun 24 2004

Keywords

Examples

			A(x) = 1 + 1*x + 5*x^2/2! + 61*x^3/3! + 1377*x^4/4! + 49721*x^5/5! +...
		

Crossrefs

Cf. A096542.

Programs

  • PARI
    a(n)=local(A=exp(x));for(i=1,n,A=exp(x*(n-i+1)*A+x*O(x^n)));n!*polcoeff(A,n)

Formula

Row sums of triangle A096542; also a(n) = A096542(n+1, 1)/(n+1) for n>=0.
Conjecture: a(n) ~ 2 * Pi * n^(2*n + 1/2) / (exp(n) * (exp(1) - 1)^n). - Vaclav Kotesovec, Dec 16 2019
Showing 1-3 of 3 results.